A tank and a pail contain a total of 5136 milliliter of water. Jacob pours 314 milliliters of water from the pail into tank. The amount of water in the tank is now 7 times what is left in the pail. How much water was in the pail at first?

Answers

Answer 1
Final answer:

To find the initial amount of water in the pail, set up a system of equations based on the total volume and the information provided after transferring some water. Solve the equations to obtain the initial quantity of 957 milliliters in the pail.

Explanation:

A student posed a problem: A tank and a pail contain a total of 5136 milliliters of water. Jacob pours 314 milliliters of water from the pail into the tank. The amount of water in the tank is now 7 times what is left in the pail. How much water was in the pail at first?

Let's denote the initial amount of water in the tank as T milliliters and in the pail as P milliliters. According to the given information, the combined quantity of water in both is 5136 milliliters:

T + P = 5136

After transferring 314 milliliters from the pail to the tank, the tank now has T + 314 milliliters, and the pail has P - 314 milliliters. It is also given that the water in the tank is now 7 times the water left in the pail:

(T + 314) = 7*(P - 314)

Now, we have a system of two equations:
   

By solving these equations, we can find the initial amount of water in the pail, P. First, modify the second equation to isolate T:

T = 7P - 2206 - 314

T = 7P - 2520

Next, substitute the expression for T from the second equation into the first equation and solve for P:

7P - 2520 + P = 5136

8P = 5136 + 2520

8P = 7656

P = 7656 / 8

P = 957 milliliters

Initially, there were 957 milliliters of water in the pail.


Related Questions

20 points!!!
Solve this system of lineal equations.separate the x- and y- values with a comma
12x=54-6y
-17x=-62-6y

Answers

The answer is:  {4, 1} .
________________________________________________________
Explanation:
________________________________________
Given the equations:
________________________________________
      "12x = 54 − 6y ;
     "-17x = -62 − 6y ;
_________________________________________
Multiply the second equation (both sides) by "-1" ;
___________________________________________
  -1*{-17x = -62 − 6y} ;

to get: 

17x = 62 + 6y ;
___________________________________________
{Note: The reason we do this is that we notice the TWO "-6y" values; and by multiplying one of the entire equations by "-1" ; we can change said equation to an equation with a "(+6y)" value; and the "(+6y)" and the "(-6y)" values cancel out to "zero" ; providing an opportunity to isolate "x"; and to solve for "x".}.
___________________________________________
Now, rewrite the two equations:
___________________________________________

       12x = 54 − 6y ;
       17x = 62 +  6y ;
___________________________________________
↔  Rewrite; and then add the two together:

       6y + 62 = 17x 
      -6y + 54 = 12x 
____________________
       0  +  116 = 29x ;

↔ 29x = 116 ;

Divide EACH SIDE of the equation by "29" ; to isolate "x" on one side of the equation ; and to solve for "x" ;
________________________________________________
   29x / 29 = 116 / 29  ;
________________________________________________
to get:
________________________________________________
           x  = 4 .
______________________________________________
Now that we have the value for "x" , which is "4" ; let us plug in "4" for "x" for either of the original two equations, to solve for "y".  In fact, let us try substituing "4" for "x" ;  for BOTH of the two original equations; to see if the value is correct.
_____________________________________________
Our original two given equations are:
_____________________________________________
      "12x = 54 − 6y ;

     "-17x = -62 − 6y ;
_____________________________________________
 Let us start with the first equation:
 ________________________
      " 12x = 54 − 6y " ;
__________________________________
When "x = 4" ; what does "y" equal ?

Plug in "4" for "x" ; to solve for "y" ;

  12(4) = 54 − 6y ;

→ 48 = 54 − 6y ;

Subtract "54" from EACH SIDE of the equation;

→ 48 − 54 = 54 − 6y − 54 ;

to get:

→  -6 = -6y ; 

→ Divide EACH side of the equation by "-6" ; to isolate "y" on one side of the equation ; and to solve for "y" ; 

→ -6/-6 = -6y / -6 ;

to get:

1 = y ;  ↔ y = 1 ;  So, we have:  x = 4, y = 1 ;  or,  {4, 1}.
______________________________________________
Let us check to see, if the second (orginal equation) holds true when "x = 4" and "y = 1 " ;
______________________________________________
The second "original equation" given is:
______________________________________________
       " -17x = -62 − 6y " ;
______________________________________________
   →    -17(4) = ?  -62  − 6(1) ?

    →  -68 = ? -62 − 6 ?

    →  -68 = ? -68 ?  Yes!
________________________________________________________
The answer is:  {4, 1} .
________________________________________________________

You have 16 Yellow beads,20 red beads,and 24 orange beads to make identical bracelets. What is the greatest number of bracelets that you can make using all beads?

Answers

Find the GCF of 16, 20, and 24

16: 1, 16; 2, 8; 4, 4
20: 1, 20; 2, 10; 4, 5
24: 1, 24; 2, 12; 3, 8; 4, 6

The GCF is 4 so 4 bracelets
Final answer:

The greatest number of identical bracelets that can be made using all the beads is 4. This is found by determining the greatest common divisor (GCD) of 16, 20, and 24, which is 4. Each bracelet will consist of 4 yellow beads, 5 red beads, and 6 orange beads.

Explanation:

The subject of this question is the mathematical concept of the greatest common divisor (GCD). In the given problem, you are tasked with finding the maximum number of identical bracelets you can make with a given number of beads. The concept of GCD is used here.

First, we need to determine the GCD of the quantities of the three different colored beads:

16 Yellow beads 20 Red beads 24 Orange beads

The GCD of 16, 20, and 24 is 4. This means the largest number of identical bracelets you can make, using all of the beads, is 4. Each bracelet will have 4 yellow beads, 5 red beads, and 6 orange beads.

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An equivalent equation has been written by multiplying the second equation by 2. 4x – 9y = 7 4x – 9y = 7 2(–2x + 3y = 4) → –4x + 6y = 8

Answers

my best guess is 
x=3/2y-2
y=2/3x+4/3
depends on which one you are solving for

Answer: answer is (-19/2,-5)


Step-by-step explanation:


solve: -3(3x+1)-41>-5(-2x+4)+5x

Answers

x < -1 should be your final answer. Hope this helps you!

Answer:

Step-fbccbbby-CBC step explanation:

Based on a sample survey, a company claims that 75% of their customers are satisfied with their products. Out of 1,176 customers, how many would you predi be satisfied?

Answers

Just multiply 1176 by the probability of satisfaction, which is 0.75:

0.75(1176) = 882

PQR has two known interior angles of 34°, and 80°. △RST has two known interior angles of 24°, and 90°. What can be determined about whether △PQR and △RST are similar?

Answers

Answer:

△PQR and △RST are not similar.

Step-by-step explanation:

In triangle △PQR, two known interior angles are 34° and 80°. So the measure of third angle is

[tex]180-34-80=66[/tex]

In triangle △RST, two known interior angles are 24° and 90°.

[tex]180-24-90=66[/tex]

Two triangles are similar if their corresponding angles are same and the corresponding sides are proportional.

Since the angles of △PQR and △RST are not same, therefore we can say that the △PQR and △RST are not similar.

solve the equation .......x/9 = 2/45 +x/10

Answers

Hello Joseph!

[tex] \frac{x}{9} = \frac{2}{45} + \frac{x}{10} Simplify both sides... 1/9 x = 2/45 + 1/10 x 1/9 x - 1/10 x = 2/45 1/90 x = 2/45 x = 2/45 * 90 x=180/45 x=4[/tex]

What does e equal in e/2 < 3? Please help. I need a quick answer.

Answers

2.718 ≈e that is the answer to your question.

At what points does the curve r(t) = ti + (4t â t2)k intersect the paraboloid z = x2 + y2? (if an answer does not exist, enter dne.)

Answers

Final answer:

To find the intersection points of the curve r(t) with the paraboloid z = x^2 + y^2, we substituted the parametric forms into the equation and solved for t, yielding the points (0, 0, 0) and (2, 0, 4).

Explanation:

The student is asking about the intersection points of a curve r(t) with a paraboloid defined by z = x2 + y2. To find these points, we must substitute the parametric forms of x, y, and z from the curve into the equation of the paraboloid and solve for t.

Given the curve r(t) = ti + (4t - t2)k, we can identify the components of the curve as x(t) = t and z(t) = 4t - t2. The y-component is missing, which implies that y = 0. Now, substituting x(t) into the paraboloid equation, we get:

z = x2 + y2

4t - t2 = t2 + 02

By solving for t, we can determine the intersection points. Simplifying the equation, we get:

0 = 2t2 - 4t

Which gives us the solutions t = 0 and t = 2. Substituting these back into r(t) gives the intersection points (0, 0, 0) and (2, 0, 4).

Help me answer this? Thanks :)

Answers

An expression is undefined when you divide by zero. A simple example is 1/0 which in english is "one over zero"

You cannot have zero in the denominator. Something like 0/1 is allowed as it is equal to 0. In other words, 0/1 = 0. But 1/0 is not allowed. 

what is 645 round to the nearest ten

Answers

The answer is 650 have a nice day
645 rounded to the nearest ten is 650

hope this helps

Miss Martin has 7000 in her savings account. Alonso has 1/10 as much money in his account as Miss Martin. How much money does Alonso have in his account.

Answers

Alonso has $700! (7000/10 or 7000*.1)

Estimate 508-113 help me please

Answers

The closest estimation is 400

You have diving lessons every fifth day and swimming lessons every third day. Today you have both lessons. In how many days will you have both lessons on the same day again?

Answers

16 days
 because 8 +8 = 16  5+3=8

if m angel 1 equal 42 and m angle 2 equal 27, then m angle APC equal

Answers

Assuming its a triangle. 42+27=69
180-69=111
so itd be 111. ;)

The measure of angle APC equals 69°

What is the measure of angle APC?

∠1 = 42°

∠2 = 27°

Angle APC is equal to the sum of angle 1 and angle 2.

∠APC = ∠1 + ∠2

= 42° + 27°

= 69°

Hence, m ∠ APC = 69°

Complete question:

if m ∠ 1 = 42 and m ∠ 2 = 27, then m ∠ APC = ?

The normal body temperature of a camel is 37°C. This temperature varies by up to 3°C throughout the day. Write and solve an absolute value inequality that represents the range of normal body temperatures (in degrees Celsius) of a camel throughout the day.

Answers

The range of normal body temperatures for a camel throughout the day is from 34°C to 40°C, inclusive.

To represent the range of normal body temperatures for a camel throughout the day, we'll use an absolute value inequality. Given that the normal body temperature is 37°C and it varies by up to 3°C, we can express this as:

|T - 37| ≤ 3

Where T represents the temperature of the camel throughout the day. This inequality ensures that the temperature remains within 3 degrees above or below the normal body temperature of 37°C.

To solve this inequality, we'll consider two cases:

1. When T - 37 is positive:

T - 37 ≤ 3

T ≤ 40

2. When T - 37 is negative:

-(T - 37) ≤ 3

-T + 37 ≤ 3

-T ≤ -34

T ≥ 34

Combining the two cases, the range of normal body temperatures for a camel throughout the day is 34°C to 40°C.

-4(n - 6) = 12

Solve the Equation.

Answers

-4(n - 6) = 12

n - 6 = -12/4   divide both sides by -4

n - 6 = -3

n = -3 + 6    add both sides by 6

n = 3

hope that helps, God bless!

jake rounded 18,752 to the nearest ten thousand which is his number

Answers

The nearest ten thousand is 20,000

20,000 is the Answer. Hope this helps.

On an average, the number of students that choose to study arts subjects at greyin tide university is 17 each year.what is the probability that exactly 13 students will take up arts in the coming year?

Answers

Unfortunately, the number of students enrolled is not known.  This must be known to calculate a numerical probability.

Suppose that there are 1000 students at the university.  Then the probability that a given student picked at random is taking an art course is 17/1000, or 0.017.

Hopefully you have a calculator capable of calculating binomial probability (which is what is involved here).

The following function should give you your answer:

binompdf(1000, 0.017, 13) = 0.0657, or roughly 7%.  The probability that 13 out of 1000 students will be taking an arts course during a given year is roughly 7%.

The probability that exactly 13 students will take up arts in the coming year is; 76.47%

What is the probability?

We are given;

Number of students that study art each year = 17

Now, we want to find the probability that 13 students will take up arts in the following year. This is;

P(13 will take art the next year) = 13/17 * 100%

P(13 will take art the next year) = 76.47%

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the sinclair family live 5.4 miles from southside middle school. how many feet away do they live?

Answers

Final answer:

The Sinclair family lives 28,512 feet away from Southside Middle School, calculated by multiplying 5.4 miles by the number of feet in one mile, which is 5,280 feet.

Explanation:

The Sinclair family lives 5.4 miles from Southside Middle School. To convert this distance from miles to feet, we use the conversion factor that 1 mile is equal to 5,280 feet. To find the distance in feet, we multiply the number of miles by the number of feet in one mile:

5.4 miles  imes 5,280 feet/mile = 28,512 feet.

Therefore, the Sinclair family lives 28,512 feet away from Southside Middle School.

Expressions that simplify to the same expression are called ____

Answers

Equivalent Expressions

Answer:

They are called equivalent expressions since they are two expression that equal the same thing.

If this helped then please mark as brainliest.

Which graph represents the solution set of the system of inequalities? {3y≥x−93x+y>−3

Answers

That is the correct graph that represents

{3y≥x−9 3x+y>−3



hope i helped =D

we have

[tex]3y\geq x-9[/tex] ----> inequality A

The solution of the inequality A is the shaded area above the solid red line

See the attached figure N [tex]1[/tex]

[tex]3x+y> -3[/tex] ----> inequality B              

The solution of the inequality B is the shaded area above the dotted blue line

See the attached figure N [tex]2[/tex]

The solution of the system of inequalities is the shaded area between the solid red line and the dotted blue line

See the attached figure N [tex]3[/tex]

therefore

the answer in the attached figure


Between white pair of numbers is a product of 200 and 89 and 7

Answers

[tex]\bf 200\cdot 89\cdot 7\implies 124600 \\\\\\ \boxed{124599}\text{\textemdash\textemdash\textemdash\textemdash\textemdash}124600\text{\textemdash\textemdash\textemdash\textemdash\textemdash}\boxed{124601}[/tex]

Find the rate of change of q with respect to p when p = 20 q 2 + 5 .

Answers

Final answer:

The rate of change of q with respect to p is the derivative of q with respect to p. However, the function seems to be incorrect as p is expressed as a function of q, not the other way around. The derivative of a typical function q = 20p^2 + 5 would be 40p.

Explanation:

The rate of change of q with respect to p is found by taking the derivative of the given function with respect to p. The function given is p = 20q^2 + 5. Unfortunately, we cannot find the derivative of p with respect to q. Instead, it seems more likely that we need to find the derivative of q with respect to p, which is typically what is intended when asked for the rate of change of one variable with respect to another. If the function was q = 20p^2 + 5, then, the derivative (rate of change) would be dq/dp = 40p. Although in your question, there may be an error as typically we would expect q to be expressed as a function of p.

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Daily output of marathon's garyville, lousiana, refinery is normally distributed with a mean of 232,000 barrels of crude oil per day with a standard deviation of 7,000 barrels. (a) what is the probability of producing at least 232,000 barrels?

Answers

50% A normal distribution is symmetric about the mean. That means that no matter what the standard deviation of a statistic, if it is normally distributed half of the time it will above the mean and half will be below. 232000 barrels is the mean and half of the time production will be above that value.

how do you know that the decimal for 2/11 repeats without end

Answers

because u just put the 2.11 in that order

Convert 50 feet per second to miles per hour.

5280 ft = 1 mi


Round to the nearest hundredth.

Answers

60*60=3600
3600*50=180,000
180,000/5280=34.09
34.09 mph.
FIrst we know that
1  second = 1/3600 hours
5280 ft = 1 miles

Which means that

50 Ft = 50/5280 miles




So the conversion 
(5/5280 miles ) / (1/3600)

= 5/5280 miles x 3600

= 34.09 miles per hour

1 1/4mi = ft, can someone explain this to me

Answers

first off, we'll convert the mixed fraction to "improper" and check about, keeping in mind that, there are 5280 feet in 1mile.

[tex]\bf \stackrel{mixed}{1\frac{1}{4}~mi}\implies \cfrac{1\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{5}{4}~mi}\\\\ -------------------------------[/tex]

[tex]\bf \begin{array}{ccll} feet&miles\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 5280&1\\ f&\frac{5}{4} \end{array}\implies \cfrac{5280}{f}=\cfrac{1}{\quad \frac{5}{4}\quad }\implies \cfrac{5280}{f}=\cfrac{\frac{1}{1}}{\quad \frac{5}{4}\quad } \\\\\\ \cfrac{5280}{f}=\cfrac{1}{1}\cdot \cfrac{4}{5}\implies \cfrac{5280}{f}=\cfrac{4}{5}\implies \cfrac{5280\cdot 5}{4}=f\implies 6600=f[/tex]

7,746.90 times x = 7,901.84 what's x

Answers

7,746.90 times x  = 7,901.84

 divide both sides by x

 x = 7,901.84 / 7,746.90

x = 1.020000258

 round to 1.02

Find and sketch the domain of the function. f(x, y, z) = 4 − x2 − y2 − z2

Answers

wages wages wages wages wages wages wages wages wages wages wages wages 

The domain of the function [tex]\(f(x, y, z) = 4 - x^2 - y^2 - z^2\)[/tex] is the set of all real numbers for [tex]\(x\)[/tex], [tex]\(y\),[/tex] and [tex]\(z\)[/tex].

To find and sketch the domain of the function [tex]\(f(x, y, z) = 4 - x^2 - y^2 - z^2\)[/tex], we need to determine the set of values for [tex]\(x\)[/tex], [tex]\(y\)[/tex], and [tex]\(z\)[/tex] for which the function is defined, i.e., the values that do not lead to any mathematical inconsistencies.

In this case, the function involves three variables, and it is defined for all real values of [tex]\(x\)[/tex], [tex]\(y\)[/tex], and [tex]\(z\)[/tex]. There are no restrictions on the domain because the square of a real number is always non-negative. Thus, [tex]\(x^2\)[/tex], [tex]\(y^2\)[/tex], and [tex]\(z^2\)[/tex] are non-negative for any real \(x\), \(y\), and \(z\).

In interval notation, we can express this as:

[tex]\[\text{Domain} = (-\infty, \infty) \times (-\infty, \infty) \times (-\infty, \infty)\][/tex]

This domain represents the entire three-dimensional space, and the function is defined for all points within this space. As such, sketching the domain involves visualizing the entire 3D space, which is an unbounded region without any specific shape or boundary.

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